Identical Parallel Machine Scheduling Considering Workload Smoothness Index

Abstract

Workload balance is significant in the manufacturing industry. However, on the one hand, some existing specific criteria cannot achieve the minimization workload imbalance of parallel machines. On the other hand, there are few algorithms in existing studies that can effectively solve the parallel machine scheduling problem with the objective of minimizing workload imbalance. Inspired by this, we investigate an identical parallel machine scheduling problem with the objective of the minimum workload smoothness index. We first establish a mathematical model for the considered problem and then linearize its objective function. We prove the NP-hardness of the problem by reducing the PARTITION problem to it, and we provide both the upper bound and lower bound of the studied problem. An efficient genetic algorithm and an improved list scheduling algorithm are also proposed to efficiently address the considered problem. The numerical results demonstrate the effectiveness of the proposed methods.